Ultrasonic inspection is used to detect and size crack-like defects in pressure vessels and pipework used in the nuclear industry. Reliable inspection can only be achieved if the inspection technique is understood, is optimised and subsequently applied correctly. Austenitic steels are used because of their corrosion resistance and toughness. Welds and centrifugally cast materials tend to crystallise with grains larger than the ultrasonic wavelength required to achieve the desired resolution in the inspection and thus appear anisotropic. Since the grains in a weld grow along the, varying, directions of maximum heat flux during cooling, the welds are inhomogeneous as well as anisotropic. We wish to understand the ultrasonic signals scattered by cracks in such inhomogeneous anisotropic materials. To calculate large numbers of cases we would like to use a relatively efficient tool: (ray tracing) and wish to incorporate the diffraction and reflection which occurs at the defect through the use of diffraction or scattering coefficients.